Half angle formula: cos(θ/2) = ±√((1 + cos θ)/2)

\cos\tfrac{\theta}{2} = \pm\sqrt{\dfrac{1 + \cos\theta}{2}}

cos(θ/2) = ±√((1 + cos θ)/2), from rearranging cos 2θ = 2cos²θ − 1. Note the plus inside the radical, against the minus in the sine version. As with sine, the sign in front is decided by the quadrant of θ/2.

Related Half Angle identities

sin θ/2 tan θ/2

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Half Angle questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Practise Half Angle Open the triangle solver

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.